Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity

Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet divergences. In this paper we demonstrate that the analogous entanglement entropies when computed within the Asymptotic Safety approach to background independent quantum gravity are perfectly free from such divergences. We argue that the divergences are an artifact due to the over-idealization of a rigid, classical spacetime geometry which is insensitive to the quantum dynamics.Comment: 19 page

Labour Market Assimilation and Over Education: The Case of Immigrant Workers in Italy

In this paper we study the assimilation of immigrants into the Italian labour market using over-education as an indicator of labour market performance. The main objective is to assess the extent to which work experience in the host country’s labour market favours the international transferability of immigrants’ human capital. Using data from the Istat Labour Force Survey for the years 2005-2007, we find that foreigners are much more likely to be over-educated than natives upon their arrival in Italy and that work experience gained in the country of origin is not valued in the Italian labour market. Moreover, we find that not even experience acquired in Italy is helpful in improving immigrants’ educational job matches, suggesting that catch-up by foreigners seems unachievable, even after they adapt their skills to the host country labour market.Assimilation, Over education

Functional and Local Renormalization Groups

We discuss the relation between functional renormalization group (FRG) and local renormalization group (LRG), focussing on the two dimensional case as an example. We show that away from criticality the Wess-Zumino action is described by a derivative expansion with coefficients naturally related to RG quantities. We then demonstrate that the Weyl consistency conditions derived in the LRG approach are equivalent to the RG equation for the $c$-function available in the FRG scheme. This allows us to give an explicit FRG representation of the Zamolodchikov-Osborn metric, which in principle can be used for computations.Comment: 19 pages, 1 figur

A functional RG equation for the c-function

After showing how to prove the integrated c-theorem within the functional RG framework based on the effective average action, we derive an exact RG flow equation for Zamolodchikov's c-function in two dimensions by relating it to the flow of the effective average action. In order to obtain a non-trivial flow for the c-function, we will need to understand the general form of the effective average action away from criticality, where nonlocal invariants, with beta functions as coefficients, must be included in the ansatz to be consistent. We then apply our construction to several examples: exact results, local potential approximation and loop expansion. In each case we construct the relative approximate c-function and find it to be consistent with Zamolodchikov's c-theorem. Finally, we present a relation between the c-function and the (matter induced) beta function of Newton's constant, allowing us to use heat kernel techniques to compute the RG running of the c-function.Comment: 41 pages, 17 figures; v2: some minor correction

Applications of the functional renormalization group in curved spacetime

Quantum field theory is the underlying framework of most of our progress in modern particle physics and has been succesfully applied also to statistical mechanics and cosmology. A basic concept of quantum field theory is the renormalization group which describes how physics changes according to the energy at which we probe the system. The functional renormalization group (fRG) for the effective average action (EAA) describes the Wilsonian integration of high momentum modes without expanding in any small parameter. As such this is a non-perturbative framework and can be used to obtain non-perturbative insights, even though some other approximations are necessary. However we are not assured that quantum field theory is the correct framework to describe physics up to arbitrary high energies. This may happen if the theory approaches an ultra violet fixed point so that all physical quantities remain finite. In this case predictivity requires a finite number of relevant directions in such a way that only a finite number of parameters needs to be fixed by the experiments. In this thesis we consider the fRG to address several problems. In chapter 1 we briefly review the fRG for the EAA deriving its flow equation and describing how theories with local symmetries can be handled and possible strategies of computation. In chapter 2 we describe how this framework can be used to investigate whether a quantum theory of gravity can be consistently built within the framework of standard quantum field theory. In particular we consider a new approximation of the flow equation for the EAA where the difference between the anomalous dimension of the fluctuating metric and the Newton\u2019s constant is taken into account. In chapter 3 we show that Weyl invariance can be maintained along the flow if a dilaton is present and if a judicious choice of the cutoff is made. This seems to contradict the standard lore according to which the renormalization group breaks Weyl invariance introducing a mass scale which is the origin of the so called trace anomaly. We analyze this in detail and show that standard results can be reobtained in a specific choice of gauge. Finally in chapter 4 we discuss a global feature of the renormalization group in two dimensions: the c-theorem. This is a global feature of the RG since it regards the whole RG trajectory from the UV to the IR. In particular we derive an exact equation for the c-function and, with some approximations, compute it explicitly in some examples. This also leads to some insights about a generic form of a truncation for the EAA. Some background material and technical details are confined to several appendices at the end of the thesis

Spatio-temporal correlation functions in scalar turbulence from functional renormalization group

We provide the leading behavior at large wavenumbers of the two-point correlation function of a scalar field passively advected by a turbulent flow. We first consider the Kraichnan model, in which the turbulent carrier flow is modeled by a stochastic vector field with a Gaussian distribution, and then a scalar advected by a homogeneous and isotropic turbulent flow described by the Navier-Stokes equation, under the assumption that the scalar is passive, i.e. that it does not affect the carrier flow. We show that at large wavenumbers, the two-point correlation function of the scalar in the Kraichnan model decays as an exponential in the time delay, in both the inertial and dissipation ranges. We establish the expression, both from a perturbative and from a nonperturbative calculation, of the prefactor, which is found to be always proportional to $k^2$. For a real scalar, the decay is Gaussian in $t$ at small time delays, and it crosses over to an exponential only at large $t$. The assumption of delta-correlation in time of the stochastic velocity field in the Kraichnan model hence significantly alters the statistical temporal behavior of the scalar at small times.Comment: 17 page

Time evolution of density matrices as a theory of random surfaces

In the operatorial formulation of quantum statistics, the time evolution of density matrices is governed by von Neumann's equation. Within the phase space formulation of quantum mechanics it translates into Moyal's equation, and a formal solution of the latter is provided by Marinov's path integral. In this paper we uncover a hidden property of the Marinov path integral, demonstrating that it describes a theory of ruled random surfaces in phase space.Comment: 31 page